Biomechanical Fuzzy Model for Analysing the Ergonomic Risk Level Associated with Upper Limb Movements

Abstract

This study proposes a decision support system that uses a fuzzy logic model to assess the risk level associated with repetitive upper limb movements during work tasks, which can lead to musculoskeletal disorders. The model considers three main sets: biomechanics, anthropometrics, and productivity. Standardised parameters were utilised to determine the risk level associated with movement. To validate the findings, a fuzzy model was applied to assess 123 female workers across three automatic high-speed production lines as a case study. The model quantifies the risks using 54 membership equations and incorporates nine linguistic variables organised into three sets: biomechanical: this includes applied force, moment force, and angle of the torso from vertical; anthropometric: this includes workers’ age and height and body mass index; and productivity: this includes working area depth, exposure time, and repetitiveness. The resulting fuzzy model, which is based on fuzzy set theory, utilises only four general fuzzy rules and allows for the evaluation of multiple workers simultaneously, providing a competitive advantage over models that rely on a large number of individual fuzzy rules to assess just one worker. The biomechanical set evaluates applied force and moment force based on productivity factors. Consequently, the behaviour of the group of 123 evaluations changed as the productivity risk value was introduced. For instance, in Test 1, which involves a low-risk task, we observed a biomechanical risk pattern that was solely related to the worker’s anthropometry. In Test 2, which presents a medium risk, the pattern of evaluations shifted, revealing behaviours that were more influenced by both anthropometric and biomechanical characteristics. Finally, in Test 3, the impact of anthropometry and biomechanics was clear in the risk assessment patterns, which aligned closely with the anthropometric. The DSS could help improve policies and work conditions.

1. Introduction

Defining the biomechanic risk level produced by an applied force developed by upper limbs during task performance can be challenging due to several factors [1]. Firstly, the level of force exerted is measured to define which movement patterns lead to musculoskeletal disorders (MSDs) [2]. Secondly, which movement patterns create a greater risk of injury during repetitive tasks is identified [3]. Finally, the anthropometric characteristics of each worker are different; thus [4], the biomechanical stress could be different for two workers who are developing the same task. Addressing this issue in this paper, a Decision Support System (DSS) is proposed that contains a biomechanical fuzzy model for analysing the ergonomic risk level associated with upper limb movements. A case study to determine the ergonomic risk levels of 123 female workers across three automatic high-speed production lines was used for validating the fuzzy model.

The Decision Support System (DSS) is an automated information system designed [5,6] to enhance ergonomics’ decision-making and improve organisational safety and health activities. It analyses and processes large amounts of biomechanic and anthropometric data, helping decision-makers to compile useful information [7] to classify the level of risk present in the workplace. This enables one to identify and solve work-related illnesses and make informed decisions to prevent them [8]. Risk refers to the effect of uncertainty related to understanding an event and its potential consequences [9,10]. From a fuzzy point of view, the risk uncertainty is non-statistical; namely, it is not a random imprecision, and the vagueness is respect to its meaning [11], e.g., the properties of occupational low risk and high risk are different, both can produce injuries and work-related illnesses [12]—the difference lies in the severity [13,14]. Therefore, to formulate a function for the fuzzy concept of risk, a membership function must be defined [15] to satisfy imprecise properties to varying the degree of risk. The membership function values are the unit interval [0.0, 1.0]. Namely, this function assigns a value between 0.0 and 1.0 to each individual in a universal set known as the Universe of Discourse “S”, indicating the membership grade of these elements in the relevant set [16]. Thus, one has a binary relationship between a set and an object; we say the object is part of the set. In fuzzy set theory, set membership is expressed in degrees [17].

On the other hand, occupational biomechanics studies tasks performed by different individuals to define the characteristics of biomechanical systems at work [18,19,20], namely, the study of how workers interact with tools, machines, and materials that can lead to musculoskeletal disorders. In biomechanical systems, workers’ bodies are viewed as a system of mechanical links [21] supported by statistical data that describe anthropometric relationships between the human body and the design of workplaces [22,23]. Therefore, anthropometric data are the foundation for developing biomechanical models that predict the forces applied during task performance; consequently, they are used to support ergonomic risk evaluations. Measuring the ergonomic risk level from a biomechanical perspective in workplaces is essential for ensuring the health and safety of workers [20,24,25]. Unsafe tasks and environments can lead to occupational illnesses [26,27].

Ergonomic evaluations that utilise fuzzy logic or a biomechanical approach have been discussed in the research literature. Some scholars have implemented a combination of anthropometrics and fuzzy logic focused on ergonomic designs; for example, Incekara [28] implemented a fuzzy method to design school furniture using anthropometric parameters. Falahati et al. [29] proposed a fuzzy logic approach to predict MSDSs, using MATLAB software and strain index to define the biomechanics of the task through 64 rules. Ramaswamy and Li [8] propose a fuzzy logic-DSS system to assess the ergonomic performance of work systems; the proposed decision support system considers physical, environmental, and sensory factors. Ani et al. [30], introduces the use of fuzzy logic to develop a strain index for minimising road accidents and fatalities. Contreras et al. [31] proposed a fuzzy interface as DSS for evaluating manual material handling. Karwowski et al. [32] modelled the electromyographic responses for 10 trunk muscles in manual material handling using fuzzy logic. Saatchi [15] provides an informative description of some of the main concepts in the field of fuzzy logic like an adaptive neuro-fuzzy inference system and fuzzy c-means clustering. Albzeirat et al. [33] presented a model for assessing the exposure to risk factors associated with MSDs based on RULA. Golabchi [34] proposes a fuzzy logic approach to posture-based ergonomic evaluation tools using RULA. However, the three most relevant studies for this investigation include those developed by Kamala and Robert [35]. They designed a fuzzy ergonomic index to evaluate a company’s ergonomics, which incorporates biomechanical aspects such as physical work, vertical reach, and clearance. However, unlike the model proposed in this work, their model does not consider anthropometric factors or productivity. Patel et al. [36] studied elbow flexion angle and torque; they analysed only biomechanic aspects. Finally, Liu et al. [37] found that the reliability of biomechanics in design needs improvement due to a lack of sufficient fundamental parameters regarding human structure. Analysing the information mentioned above, it becomes evident that previous investigations have not simultaneously addressed fuzzy logic methods in combination with anthropometric, biomechanical, and productivity factors. A comparison between fuzzy models is presented in

Table 1. Comparison of characteristics between fuzzy logic models.

Authors	Accessible Software	Includes Biomechanic Model	Includes Anthropometric Workers’ Characteristics	Includes Productivity Work Characteristics	Reduced Fuzzy Rules	Multiple Assessment
Ramaswamy and Li [8]				✓
Incekara [28]				✓
Falahati et al. [29]				✓
Ani et al. [30]				✓
Contreras et al. [31]				✓
Karwowski et al. [32]		✓	✓
Saatchi [15]					✓	✓
Albzeirat et al. [37]	✓	✓				✓
Golabchi [34]				✓
Kamala and Robert [35]		✓	✓
Patel et al. [36]		✓	✓
Liu et al. [37]		✓	✓
Biomechanical fuzzy model proposed in this paper	✓	✓	✓	✓	✓	✓

The symbol ✓ indicates the characteristics of the fuzzy model.

.

Therefore, this paper proposes new scenarios for analysing productivity from a biomechanic and anthropometric point of view. Thus, this article sets a new frame of reference for studying ergonomic risk levels.

This article reports a proposed biomechanical fuzzy model for analysing the ergonomic risk level associated with upper limb movements inside workplaces by analysing three main groups of sets: biomechanics, anthropometrics, and productivity, which directly impact the quality of the workers’ lives. The DSS was developed in Excel and applied to evaluate 123 female workers at the same time. This paper’s contribution and research’s novelty lie in the following:

• The design of a fuzzy logic model to define and quantify workers’ anthropometric characteristics to determine the biomechanic risk level using only four general rules.
• The fuzzification of ergonomic risk using standardised data relating to biomechanics, anthropometrics, and productivity.
• A proposed DSS fuzzy model for implementing multiple assessments that establishes a record for measuring and monitoring the risk level at work using biomechanics and anthropometric characteristics.

2. Materials and Methods

2.1. Problem Description

The relationship between biomechanics, anthropometrics, and productivity in assessing the risk associated with upper limb movements is often overlooked. To address this issue, this study proposes a fuzzy logic model to help prevent musculoskeletal disorders (MSDs). A significant challenge arose in defining the membership level of each fuzzy set—productivity, anthropometry, and biomechanics—within an infinite Universe of Discourse S called “Task Movements”. This framework aims to determine a combined degree of membership regarding risk, as illustrated in Figure 1. Under these conditions, a typical fuzzy model would require 3⁹ combinations of fuzzy rules (equivalent to 19,683 fuzzy rules). Therefore, a model is required that simplifies the number of rules to be developed, considering the relationship between these three sets and their subsets. The proposed model includes fuzzy variables to specify the level of risk in one arm movement through membership equations defined as elements of association from a biomechanical point of view. The subsequent sections describe this fuzzy process to better understand how it works.

2.2. Case Study

This investigation considers the biomechanics and anthropometric characteristics of 123 Mexican female workers who work in three automatic high-speed lines designed to fill dialysis bags with a liquid mixture. Each worker had a daily goal of producing 5000 bags per shift lasting 420 min, during which they worked while standing. This work method was leading to shoulder issues. To solve this problem, a fuzzy biomechanic model that minimises the risk level but maximises productivity was proposed using the workers’ anthropometric and biomechanics characteristics.

The anthropometric study included age (A), height (H), and body mass index (BMI); the results are shown in Appendix C. The biomechanical study included the moment force (MF), applied force (AF), and angle θ (arm position concerning the trunk due to work position), estimated for each worker; the results are provided in Appendix D. In the proposed model, the content of both studies represents two sets of data; the third set is given by the work task that seeks high productivity, as is depicted in Figure 2.

The model results indicate the movement risk level associated with specific characteristics based on work task parameters. By inputting various task parameters, one can identify the optimal combination that enhances productivity while minimising the risk of developing musculoskeletal disorders (MSDs).

2.3. Biomechanic Fuzzy Logic Model

This paper proposes a fuzzy model to properly define the biomechanical risk level in repetitive upper limb movements. The goal is to identify the impact of work task characteristics that can lead to the development of MSDs. The fuzzy logic method seeks new ways to use biomechanical and anthropometric characteristics for injury prevention. The biomechanical equations used are applicable across different genders and diverse populations. The proposed model incorporates anthropometric data as input, making it adaptable to geographic diversity. This flexibility allows the model to be easily applied in various production environments.

A fuzzy system is designated an expert system when utilised for advising, diagnosing, or reasoning and usually consists of three major components [11]:

• Fuzzification.
• Decision Support System (DSS).
• Defuzzification.

2.3.1. Fuzzification

Fuzzification was employed to convert task movements (universe of discourse) into degrees of biomechanical risk levels, expressed in linguistic terms. Each subset (MF, AF, θ, A, H, BMI, ET, R, and D) was represented by a fuzzy subset that determined the membership level for each category (Biomechanics, Anthropometrics, and Productivity) using a membership function, as illustrated in Figure 3. This process of fuzzification allows for the transformation of scalar values (crisp values) into linguistic variables, facilitating fuzzy reasoning [11]. The linguistic variables express quantities or values associated with specific levels of risk, as defined in Equations (1) and (2). The process of fuzzification required building one fuzzy equation for each subset. A total of nine fuzzy equations from Equation (A1) to Equation (A9) are provided in Appendix A, “Linguistic Variables”, one for each subset.

$${MV}_{RL}\left(x\right)=\left\{\begin{array}{c}1.0 IF x \in HRL \\ 0.5 IF x aceptable degree of\in MRL\\ 0.0 IF x \notin Absence of RL\end{array}\right.$$

(1)

$${MV}_{RL}\left(x\right)=\left\{\begin{array}{c}1.0 IF 2 points\le x\le 4 points THEN HRL \\ 0.5 IF 1 points\le x\le 3 points THEN MRL\\ 0.0 IF 0 points\le x\le 2 points THEN LRL\end{array}\right.$$

(2)

The theoretical basis for designing the membership function for each equation in Appendix A, “Linguistic Variables”, is diverse.

Table 2. Theoretical basis for membership functions.

Membership Function	Theoretical Basis	Parameters
		Low Risk	Medium Risk	High Risk
Moment force (MF)	Chaffin et al. [21,38]	0 to 30 Nm	15 to 45 Nm	30 to 60 Nm
Applied force (AF)	ISO 11228-3 [39]	0 to 25 N	15 to 45 N	35 to 80 N
Angle (θ) from vertical torso	Chaffin et al. [21]	0 to 40 degrees	25 to 70 degrees	55 to 180 degrees
Age (A)	NOM 036-1 STPS [40]	18 to 35 years old	20 to 50 years old	35 to 65 years old
Height (H)	ISO 14738 [23]	190 to 160 cm	170 to 150 cm	1500 to 140 cm
Body mass index (BMI)	NIH [41]	18 to 30 kg/m2	25 to 35 kg/m2	30 to 60 kg/m2
Exposition time	ISO 11228-3 [39]	0 to 240 min	30 to 420 min	240 to 480 min
Working area depth	ISO 14738 [23]	170 to 300 cm	230 to 370 cm	300 to 500 cm
Repetitiveness	ISO 11228-3 [39]	0 to 700 repetitions	200 to 1200 repetitions	700 to 1500 repetitions

presents the theoretical source of each variable.

2.3.2. Decision Support System (DSS)

Membership Functions and Graphics

This system consisted of fuzzy implications (IF-THEN rules) for assessing biomechanical, anthropometric, and work task criteria based on system inputs and internal knowledge, as defined above. The outcome of this processing is a fuzzy solution expressed as a membership value. The degree of membership Y (µMB_RL) of the variable x in the fuzzy set “Movement” is given by the following Equations (3) to (8):

$${\mu MV}_{LOW}=1, \mathrm{OR}$$

(3)

$${\mu MV}_{LOW}=-x+2 \mathrm{OR}$$

(4)

$${\mu MV}_{MEDIUM}=x-1 \mathrm{OR}$$

(5)

$${\mu MV}_{MEDIUM}=-x+3 \mathrm{OR}$$

(6)

$${\mu MV}_{HIGH}=0.x-2 \mathrm{OR}$$

(7)

$${\mu MV}_{HIGH}=1,$$

(8)

Figure 3 is a simple graphical expression of straight lines that defines degrees of membership from 0.0 to 1.0 for each level of risk. The linguistic variables are represented by Equations (3) to (8). The crisp values represent the level of risk; therefore, 0 to 2 represents a low risk, 1 to 3 represents a medium risk, and 2 to 4 represents a high risk. Appendix B, “Membership equations”, defines and provides fifty-four membership equations (six equations for each subset) and nine graphics to cover all linguistic variables.

Fuzzy Operations

Four operations between fuzzy sets were required to combine sets in which we managed to minimise the level of risk and maximise productivity: containment, concentration, dilution, and intersection. Thus, these subsets have a shared risk level membership different from the individual risk level.

• The subset θ is part of two fuzzy subsets; it is contained in MF and AF. The results of moment and force depend on θ. As a result, the subsets MF and AF have a conditional relationship with θ defined as follows:

  $$CONDITIONATED SUBSETS=\theta \subset MF AND \theta \subset AF$$

  $$S=Arm Movement (Universe of Discourse)$$

  $$\theta =Fuzzy subset in MF and AF$$

  $$X,Y=are MF and AF in S$$

  $$\mathrm{If} MF\cap AF is a binary relation X\times Y \mathrm{then}$$

  $$F=\theta o MF\cap AF$$

  $${\mu }_F\left(Y’\right)=MAX(MIN\left(X/Y\right), {\mu }_{\theta }\left(Y\right))$$

  (9)
• Considering the phrases maximising productivity and minimising risk level, from a fuzzy logic perspective, one needs to emphasise the members of the subset ET, R, and D and de-emphasise MF and AF to do these two definitions are presented:

Definition 1.

In the representation of linguistic modifiers (hedges), the operation of concentration is given by P², normally called square law [11].

Definition 2.

In the representation of linguistic hedges, the operation of dilution is given by P^½, normally called the square root function law [11].

From which one has,

$${\mu ET}^2\left(x\right)$$

(10)

$${\mu R}^2\left(x\right)$$

(11)

$${\mu D}^2\left(x\right)$$

(12)

$${\mu MF}^{{\displaystyle \frac{1}{2}}}(x)$$

(13)

$${\mu AF}^{{\displaystyle \frac{1}{2}}}(x)$$

(14)

• The intersection of the three fuzzy subsets, for example, MF, AF and θ, is a new subset containing all the risk levels that are members of three sets, and the interpretation is the same for the other intersections expressed as

$$MF\cap AF\cap \theta$$

(15)

$$A\cap H\cap BMI$$

(16)

$$ET\cap R\cap D$$

(17)

From which one has,

$$MF\cap AF\cap \theta =\left\{x|\left(xϵMF and xϵAF and xϵ\theta \right)\right\}$$

(18)

$$A\cap H\cap BMI=\left\{y|\left(yϵA and yϵH and yϵBMI\right)\right\}$$

(19)

$$ET\cap R\cap D=\left\{z|\left(zϵET and zϵR and zϵD\right)\right\}$$

(20)

$$INTERSECTION OF SETS, Biomechanics\cap Anthropometrics \cap Productivity$$

$$S=Arm Movement (Universe of Discourse)$$

$$MF, AF, \theta =Fuzzy subset in Biomechanics Set \left(\mathrm{Biomechanics}\right)$$

$$A,H,BMI=Fuzzy subset in Anthropometric Set \left(\mathrm{Anthropometrics}\right)$$

$$ET,R,D=Fuzzy subset in Productivity Set \left(\mathrm{Productivity}\right)$$

$$X,Y,Z are Bio and Anth and \left(Prod\right) in S$$

$$\mathrm{then}$$

$$(\theta o MF\cap AF )\cap (A\cap H\cap BMI)\cap (ET\cap R\cap D)$$

(21)

$${\mu }_{LOW}\left(Y\right)=MAX\left(MIN\right(X/Y/Z),({\mu }_{LOW}\left(X\right),({\mu }_{LOW}\left(Y\right),\left({\mu }_{LOW}\left(Z\right)\right))$$

(22)

$${\mu }_{MEDIUM}\left(Y\right)=MAX\left(MIN\right(X/Y/Z),({\mu }_{MEDIUM}\left(X\right),({\mu }_{MEDIUM}\left(Y\right),\left({\mu }_{MEDIUM}\left(Z\right))\right)$$

(23)

$${\mu }_{HIGH}\left(Y\right)=MAX\left(MIN\right(X/Y/Z),({\mu }_{HIGH}\left(X\right),({\mu }_{HIGH}\left(Y\right),\left({\mu }_{HIGH}\left(Z\right)\right)))$$

(24)

2.3.3. Rules Definition

To build the linguistic model, it was necessary to define IF-THEN rules. The objective was to define different risk levels of upper limb movements using three sets (biomechanics, anthropometric, and productivity) and nine variables (moment force, applied, force, angle, age, height, body mass index, exposition time, working area depth, and repetitiveness). Applying fuzzy set theory, the fuzzy model proposed incorporates four generic fuzzy rules that establish the ergonomic risk level as follows:

General Biomechanical Rule

$$IF MF\left(x\right) AND AF\left(x\right) AND \theta \left(x\right) THEN {BIOM}_{RL}\left(x\right)$$

(25)

General Anthropometric Rule

$$IF A\left(y\right) AND H\left(y\right) AND BMI\left(y\right) THEN {ANTHR}_{RL}\left(y\right)$$

(26)

General Productivity Rule

$$IF ET\left(z\right) AND R\left(z\right) AND D\left(z\right) THEN {PROD}_{RL}\left(z\right)$$

(27)

General Risk Level Rule

$$IF BIOM\left(x\right) AND ANTHR\left(y\right) AND PROD\left(z\right) THEN {MV}_{RL}\left(x\right)$$

(28)

where x, y, and z are any value in S = Arm Movement (Universe of Discourse).

This contribution distinguishes the proposed model from other fuzzy models that require numerous specific rules.

2.3.4. Defuzzification

This procedure transformed a fuzzy solution (membership value) into a single output representing a biomechanical risk level. Ultimately, returning to a more precise or “crisp” world is generally necessary. This return is achieved through a process known as defuzzification. Defuzzification involves interpreting the membership degrees of fuzzy sets into specific decisions or real values [17]. Through this process, a second mapping converts fuzzy signals into their exact real-world counterparts. The lineal equation for the defuzzification was

$$RL=4\left({MV}_{RL}\left(x\right)\right)$$

(29)

3. Results

This section presents the results of the fuzzy logic model for assessing arm movement during task performance. It considers four key assumptions:

• The global reference frame was defined in a two-dimensional plane (2D), specifically regarding the horizontal plane (x-axis) of flexion motion and the frontal plane when the hand reaches for an object (see Appendix D).
• The anthropometric data were collected using information from 123 female workers (see

  Table A2. Results from the anthropometric study of 122 female workers.

  No	H (m)	SH (m)	TBM (kg)	UAL (m)	FAL (m)	HdL (m)	No	H (m)	SH (m)	TBM (kg)	UAL (m)	FAL (m)	HdL (m)
  1	1.60	1.31	53.2	0.298	0.234	0.173	62	1.59	1.30	71.1	0.296	0.232	0.172
  2	1.43	1.17	58.3	0.266	0.209	0.154	63	1.54	1.26	58.6	0.286	0.225	0.166
  3	1.53	1.25	57.9	0.285	0.223	0.165	64	1.49	1.22	64.9	0.277	0.218	0.161
  4	1.54	1.26	60.2	0.286	0.225	0.166	65	1.64	1.34	62.6	0.305	0.239	0.177
  5	1.64	1.34	70.1	0.305	0.239	0.177	66	1.49	1.22	64.4	0.277	0.218	0.161
  6	1.44	1.18	56.0	0.268	0.210	0.156	67	1.59	1.30	66.9	0.296	0.232	0.172
  7	1.57	1.28	69.0	0.292	0.229	0.170	68	1.54	1.26	46.8	0.286	0.225	0.166
  8	1.59	1.30	71.1	0.296	0.232	0.172	69	1.62	1.33	78.7	0.301	0.237	0.175
  9	1.54	1.26	58.6	0.286	0.225	0.166	70	1.43	1.17	60.1	0.266	0.209	0.154
  10	1.49	1.22	64.9	0.277	0.218	0.161	71	1.58	1.29	71.1	0.294	0.231	0.171
  11	1.64	1.34	62.6	0.305	0.239	0.177	72	1.59	1.30	64.5	0.296	0.232	0.172
  12	1.49	1.22	64.4	0.277	0.218	0.161	73	1.68	1.37	62.3	0.312	0.245	0.181
  13	1.65	1.35	70.8	0.307	0.241	0.178	74	1.49	1.22	52.3	0.277	0.218	0.161
  14	1.54	1.26	46.8	0.286	0.225	0.166	75	1.51	1.24	56.2	0.281	0.220	0.163
  15	1.62	1.33	78.7	0.301	0.237	0.175	76	1.56	1.28	61.2	0.290	0.228	0.168
  16	1.43	1.17	60.1	0.266	0.209	0.154	77	1.5	1.23	56.4	0.279	0.219	0.162
  17	1.58	1.29	71.1	0.294	0.231	0.171	78	1.56	1.28	75.5	0.290	0.228	0.168
  18	1.59	1.30	64.5	0.296	0.232	0.172	79	1.56	1.28	69.6	0.290	0.228	0.168
  19	1.63	1.33	60.0	0.303	0.238	0.176	80	1.54	1.26	53.6	0.286	0.225	0.166
  20	1.65	1.35	70.0	0.307	0.241	0.178	81	1.56	1.28	57.7	0.290	0.228	0.168
  21	1.51	1.24	56.2	0.281	0.220	0.163	82	1.68	1.37	72.2	0.312	0.245	0.181
  22	1.63	1.33	68.5	0.303	0.238	0.176	83	1.49	1.22	80.7	0.277	0.218	0.161
  23	1.5	1.23	56.4	0.279	0.219	0.162	84	1.53	1.25	63.5	0.285	0.223	0.165
  24	1.56	1.28	75.5	0.290	0.228	0.168	85	1.66	1.36	73.9	0.309	0.242	0.179
  25	1.56	1.28	69.6	0.290	0.228	0.168	86	1.53	1.25	67.3	0.285	0.223	0.165
  26	1.54	1.26	53.6	0.286	0.225	0.166	87	1.55	1.27	67.4	0.288	0.226	0.167
  27	1.56	1.28	57.7	0.290	0.228	0.168	88	1.6	1.31	65.0	0.298	0.234	0.173
  28	1.61	1.32	53.2	0.299	0.235	0.174	89	1.55	1.27	63.0	0.288	0.226	0.167
  29	1.44	1.18	58.3	0.268	0.210	0.156	90	1.57	1.28	65.8	0.292	0.229	0.170
  30	1.52	1.24	57.9	0.283	0.222	0.164	91	1.5	1.23	69.2	0.279	0.219	0.162
  31	1.54	1.26	60.2	0.286	0.225	0.166	92	1.48	1.21	61.8	0.275	0.216	0.160
  32	1.65	1.35	70.1	0.307	0.241	0.178	93	1.48	1.21	59.7	0.275	0.216	0.160
  33	1.6	1.31	65.5	0.298	0.234	0.173	94	1.56	1.28	67.0	0.290	0.228	0.168
  34	1.58	1.29	69.0	0.294	0.231	0.171	95	1.49	1.22	60.9	0.277	0.218	0.161
  35	1.6	1.31	71.1	0.298	0.234	0.173	96	1.5	1.23	63.4	0.279	0.219	0.162
  36	1.54	1.26	58.6	0.286	0.225	0.166	97	1.52	1.24	75.8	0.283	0.222	0.164
  37	1.47	1.20	64.9	0.273	0.215	0.159	98	1.53	1.25	63.5	0.285	0.223	0.165
  38	1.6	1.31	62.6	0.298	0.234	0.173	99	1.67	1.37	75.2	0.311	0.244	0.180
  39	1.5	1.23	64.4	0.279	0.219	0.162	100	1.53	1.25	60.7	0.285	0.223	0.165
  40	1.57	1.28	62.6	0.292	0.229	0.170	101	1.6	1.31	65.2	0.298	0.234	0.173
  41	1.54	1.26	45.7	0.286	0.225	0.166	102	1.6	1.31	60.5	0.298	0.234	0.173
  42	1.62	1.33	68.7	0.301	0.237	0.175	103	1.58	1.29	57.4	0.294	0.231	0.171
  43	1.43	1.17	50.1	0.266	0.209	0.154	104	1.57	1.28	65.8	0.292	0.229	0.170
  44	1.58	1.29	70.0	0.294	0.231	0.171	105	1.65	1.35	70.1	0.307	0.241	0.178
  45	1.59	1.30	64.5	0.296	0.232	0.172	106	1.48	1.21	50.9	0.275	0.216	0.160
  46	1.6	1.31	67.2	0.298	0.234	0.173	107	1.5	1.23	59.7	0.279	0.219	0.162
  47	1.56	1.28	58.3	0.290	0.228	0.168	108	1.62	1.33	70.5	0.301	0.237	0.175
  48	1.51	1.24	56.2	0.281	0.220	0.163	109	1.49	1.22	55.6	0.277	0.218	0.161
  49	1.47	1.20	60.3	0.273	0.215	0.159	110	1.68	1.37	73.1	0.312	0.245	0.181
  50	1.5	1.23	56.4	0.279	0.219	0.162	111	1.55	1.27	50.8	0.288	0.226	0.167
  51	1.56	1.28	75.5	0.290	0.228	0.168	112	1.53	1.25	62.8	0.285	0.223	0.165
  52	1.56	1.28	69.6	0.290	0.228	0.168	113	1.62	1.33	74.1	0.301	0.237	0.175
  53	1.54	1.26	53.6	0.286	0.225	0.166	114	1.5	1.23	57.8	0.279	0.219	0.162
  54	1.56	1.28	57.7	0.290	0.228	0.168	115	1.49	1.22	62.9	0.277	0.218	0.161
  55	1.6	1.31	53.2	0.298	0.234	0.173	116	1.55	1.27	64.3	0.288	0.226	0.167
  56	1.43	1.17	58.3	0.266	0.209	0.154	117	1.58	1.29	57.8	0.294	0.231	0.171
  57	1.53	1.25	57.9	0.285	0.223	0.165	118	1.64	1.34	78.8	0.305	0.239	0.177
  58	1.54	1.26	60.2	0.286	0.225	0.166	119	1.5	1.23	65.3	0.279	0.219	0.162
  59	1.64	1.34	70.1	0.305	0.239	0.177	120	1.63	1.33	65.7	0.303	0.238	0.176
  60	1.63	1.33	78.4	0.303	0.238	0.176	121	1.64	1.34	58.1	0.305	0.239	0.177
  61	1.57	1.28	69.0	0.292	0.229	0.170	122	1.49	1.22	55.0	0.277	0.218	0.161

  in Appendix C). The segment fractions as a percentage of H and BMI were taken from [42,43], as shown in

  Table A1. Anthropometric segment fractions for upper limbs [44].

  Description	Upper Arm Glenohumeral Axis/Elbow Axis	Forearm -Elbow Axis/Ulnar Styloid	Hand Wrist Axis/Knuckle II Middle Finger
  Segment Mass (SM)/Total Body Mass (TBM)	0.028	0.016	0.006
  Centre of Mass (CoM)—Segment Length-Proximal	0.436	0.43	0.506

  .
• The DSS result represents the risk level from the intersection between the productivity, biomechanic, and anthropometric sets, as defined in Equation (21). It considers the concentration operation (Equations (10)–(12)) of the elements in the productivity set and the dilution operation (Equations (13) and (14)) of the biomechanical set.
• The work task is limited to handling low loads at high frequency with a maximum mass manipulated of 3 kg.

As previously mentioned, the DSS of this proposed model does not rely on fuzzy rules. It only requires the input data established for the productivity set. The membership is computed immediately, representing the risk level for each of the 123 workers according to their anthropometric characteristics. In Test 1 (see Figure 4), a task previously classified as very low risk was evaluated using the following specific values: ET = 60 min, R = 60 movements, D = 250 mm, and holding a 1 kg mass in hand. The Decision Support System (DSS), designed in Excel, displays several key pieces of information. It features a section for inputting biomechanical parameters—specifically the deltoids’ insertion distance and angle—and productivity metrics. The system computes and presents the resultant risk level, alongside four graphics that evaluate risk for each worker based on the following criteria: (a) Biomechanical Membership: This starts from 0.35 and ranges up to 1.00, indicating an increase from medium to high biomechanical impact. Workers are organised according to their height and Body Mass Index (BMI), with taller and heavier individuals positioned at the end. (b) Anthropometric Membership: This graphic illustrates the anthropometric characteristics of the workers. (c) Intersection Membership: This graphic displays the overlap among the three subsets—biomechanics, anthropometrics, and productivity. (d) Resultant Risk Level: Finally, this graph shows the defuzzified risk level for each worker.

Test 2 adjusted the parameters to represent a higher risk than the previous test. The settings included an exposition time (ET) of 120 min, 240 repetitions (R), a depth (D) of 300 mm, and the addition of a 2 kg mass held in hand. As the manipulated mass increased to 2 kg, the membership level in graph (a) also increased, approaching a maximum value of 1. The minimum value observed was 0.45, as shown in Figure 5. The graph labelled (b) remains unchanged because it represents the same group of workers. In contrast, graph (c) shows an increase in membership values from 0.38 to 0.41, indicating that there are workers with varying risk levels. Finally, in graph (d), the defuzzified result is defined as 1.71 points, which indicates a low-risk level.

In Test 3 (see Figure 6), high-risk values were recorded as follows: ET = 480 min, R = 1200 movements, D = 400 mm, while holding a 3 kg weight. Under these task conditions, significant changes were observed in evaluation behaviour. In graph (a), the minimum membership level was increased from 0.45 (for 2 kg) to 0.67, closer to the value of 1.0, reflecting the increased weight handled, now at 3 kg. The graph labelled (b) remains unchanged because it represents the same group of workers. In contrast, graph (c) demonstrates an increase in membership values from 0.45 to 0.89. This pattern aligns with that observed in the anthropometric graphic. An example of resultant memberships from biomechanic and anthropometric study are presented in

Table 3. Example of resultant membership from the θoMF∩AF subset.

Worker	MF	MFLOW	MFMED	MFHIGH	AF	AFLOW	AFMED	AFHIGH	θ	θLOW	θMED	θHIGH	θoMF∩AF
W1	40.06	0.00	0.32	0.50	49.22	0.00	0.00	0.95	32.53	0.37	0.38	0.00	0.57
W2	41.30	0.00	0.23	0.57	50.74	0.00	0.00	1.00	35.52	0.22	0.53	0.00	0.81
W3	34.43	0.00	0.69	0.22	42.30	0.00	0.18	0.49	33.71	0.31	0.44	0.00	0.53
W4	40.06	0.00	0.32	0.50	49.22	0.00	0.00	0.95	33.54	0.32	0.43	0.00	1.00
W5	41.30	0.00	0.23	0.57	50.74	0.00	0.00	1.00	31.90	0.41	0.34	0.00	0.66
W6	38.75	0.00	0.40	0.44	47.50	0.00	0.00	0.84	35.33	0.23	0.52	0.00	0.52
W7	40.34	0.00	0.30	0.52	49.45	0.00	0.00	0.97	33.03	0.35	0.40	0.00	0.65
W8	45.85	0.00	0.00	0.79	55.82	0.00	0.00	1.00	32.70	0.37	0.38	0.00	0.63
W9	42.60	0.00	0.15	0.63	51.86	0.00	0.00	1.00	33.54	0.32	0.43	0.00	0.67
W10	43.95	0.00	0.06	0.70	53.39	0.00	0.00	1.00	34.41	0.28	0.47	0.00	0.91

and

Table 4. Example of resultant membership from the A∩H∩BMI subset.

Worker	Age	ALOW	AMED	AHIGH	Height	HHIGH	HMED	HLOW	BMI	BMILOW	BMIMED	BMIHIGH	A∩H∩BMI
W1	21	0.93	0.07	0.00	143	0.70	0.20	0.00	28.51	0.00	0.70	0.00	0.70
W2	48	0.00	0.13	1.00	143	0.70	0.20	0.00	29.39	0.00	0.88	0.00	0.70
W3	48	0.00	0.13	1.00	143	0.70	0.20	0.00	24.50	0.55	0.00	0.00	0.55
W4	21	0.93	0.07	0.00	143	0.70	0.20	0.00	28.51	0.00	0.70	0.00	0.70
W5	55	0.00	0.00	1.00	143	0.70	0.20	0.00	29.39	0.00	0.88	0.00	0.70
W6	37	0.00	0.87	0.20	144	0.60	0.27	0.00	27.01	0.00	0.40	0.00	0.40
W7	26	0.60	0.40	0.00	144	0.60	0.27	0.00	28.12	0.00	0.62	0.00	0.60
W8	47	0.00	0.20	1.00	147	0.30	0.47	0.00	30.03	0.00	0.99	0.00	0.47
W9	21	0.93	0.07	0.00	147	0.30	0.47	0.00	27.91	0.00	0.58	0.00	0.47
W10	42	0.00	0.53	0.70	148	0.20	0.54	0.00	28.21	0.00	0.64	0.00	0.54

, and the extended results for all workers are present in Appendix E. In Table 3, the first ten resultant memberships by subset are shown, considering for each subset the moment, force, and angle obtained in the study and their corresponding memberships by low, medium, and high risk, as well as, in Table 4, the first ten resultant memberships by subset, which are shown considering for each subset the age, height, and BMI obtained in the study and their corresponding membership by low, medium, and high risk. These results indicate that workers’ biomechanical and anthropometric characteristics significantly impact the level of ergonomic risk. The results of the other 30 tests are presented in

Table 5. Test from different combinations of work tasks considering one repetition by minute.

Test	ET (s)	R (Mov)	D (mm)	MASS (kg)	Biomechanic Membership θ o (MF∩AF)	AND	Anthropometrics Membership θ o(MF∩AF) ∩ (A∩H∩BM)	AND	Productivity Membership θ o(MF∩AF) ∩ (A∩H∩BM) ∩ (ET∩R∩D)	Maximum Risk Level	Risk Level Average
1	60	60	200	1	0.43 to 1.00		0.34 to 0.91		0.14	0.57	Very Low
2	60	60	200	2	0.47 to 1.00		0.34 to 0.91		0.14	0.57	Very Low
3	60	60	200	3	0.67 to 1.00		0.34 to 0.91		0.14	0.57	Very Low
4	120	120	300	1	0.44 to 1.00		0.34 to 0.91		0.34 to 0.43	1.71	Low
5	120	120	300	2	0.47 to 1.00		0.34 to 0.91		0.34 to 0.43	1.71	Low
6	120	120	300	3	0.67 to 1.00		0.34 to 0.91		0.34 to 0.43	1.71	Low
7	180	180	200	1	0.43 to 1.00		0.34 to 0.75		0.028	1.12	Low
8	180	180	200	2	0.47 to 1.00		0.34 to 0.91		0.028	1.12	Low
9	180	180	200	3	0.67 to 1.00		0.34 to 0.91		0.028	1.12	Low
10	240	240	300	1	0.43 to 1.00		0.34 to 0.91		0.35 to 0.68	2.70	Medium
11	240	240	300	2	0.47 to 1.00		0.34 to 0.91		0.35 to 0.68	2.70	Medium
12	240	240	300	3	0.67 to 1.00		0.34 to 0.91		0.35 to 0.68	2.70	Medium
13	300	300	200	1	0.43 to 1.00		0.34 to 0.91		0.35 to 0.41	1.64	Low
14	300	300	200	2	0.47 to 1.00		0.34 to 0.91		0.35 to 0.41	1.64	Low
15	300	300	200	3	0.67 to 1.00		0.34 to 0.91		0.35 to 0.41	1.64	Low
16	360	360	300	1	0.43 to 1.00		0.34 to 0.91		0.32	1.27	Low
17	360	360	300	2	0.47 to 1.00		0.34 to 0.91		0.32	1.27	Low
18	360	360	300	3	0.67 to 1.00		0.34 to 0.91		0.32	1.27	Low
19	420	420	200	1	0.43 to 1.00		0.34 to 0.91		0.35 to 0.50	2.00	Medium
20	420	420	200	2	0.47 to 1.00		0.34 to 0.91		0.35 to 0.50	2.00	Medium
21	420	420	200	3	0.67 to 1.00		0.34 to 0.91		0.35 to 0.50	2.00	Medium
22	480	480	300	1	0.43 to 1.00		0.34 to 0.91		0.35 to 0.68	2.70	Medium
23	480	480	300	2	0.47 to 1.00		0.34 to 0.91		0.35 to 0.68	2.70	Medium
24	480	480	300	3	0.67 to 1.00		0.34 to 0.91		0.35 to 0.68	2.70	Medium
25	540	540	200	1	0.43 to 1.00		0.34 to 0.91		0.35 to 0.75	3.06	High
26	540	540	200	2	0.47 to 1.00		0.34 to 0.91		0.35 to 0.75	3.06	High
27	540	540	200	3	0.67 to 1.00		0.34 to 0.91		0.35 to 0.75	3.06	High
28	600	600	300	1	0.43 to 1.00		0.34 to 0.91		0.35 to 0.75	3.17	High
29	600	600	300	2	0.47 to 1.00		0.34 to 0.91		0.35 to 0.75	3.17	High
30	600	600	300	3	0.67 to 1.00		0.34 to 0.91		0.35 to 0.75	3.17	High

, considering the biomechanic parameters of deltoid insertion distance of 15 cm and deltoid angle of 18° and different combinations of work tasks considering one repetition by minute.

The resultant statistics from the arm movement assessment of 123 production line workers categorised by linguistic variable are as follows:

• Anthropometrics
  • Age: between 18 to 20 years old, low risk, 6.5%; between 21 to 45 years old, medium risk, 69%; and between 46 to 65 years old, high risk, 24.5%.
  • Height: between 1.40 m to 1.50 m, high risk, 25%, and between 1.41 m to 1.70 m, medium risk, 75%.
  • BMI: between 18 kg/m² to 25 kg/m², low risk, 48%; between 26 kg/m² to 35 kg/m², medium risk, 51%; and 36 kg/m² to 60 kg/m², high risk, 1%.
• Biomechanics
  • Age: between 18 to 20 years old, low risk, 6.5%; between 21 to 45 years old, medium risk, 69%; and between 46 to 65 years old, high risk, 24.5%.
  • Height: between 1.40 m to 1.50 m, high risk, 25%, and between 1.41 m to 1.70 m, medium risk, 75%.
• Productivity: Thirty-three tests were conducted (see Table 5) on 123 workers, combining the characteristics of nine linguistic variables to simulate various working conditions, resulting in a total of 4059 combinations, with the following results:
  • Very low risk: 369 results representing 9%.
  • Low risk: 1599 results representing 39.4%.
  • Medium risk: 1230 results representing 30.4%.
  • High risk: 861 results representing 21.2%.

4. Discussion

To effectively discuss the contributions of the current investigation, it is necessary to compare the present situation. However, existing risk assessments such as RULA, REBA, and similar evaluations are based on biomechanical models that are either not clearly defined or not publicly available. Additionally, these assessments do not take into account the anthropometric characteristics of workers. As a result, the risk values they produce are merely approximations. In contrast, the proposed model calculates biomechanical values based on the specific anthropometric characteristics of individual workers. This makes direct comparison between the models not applicable. On the other hand, the proposed fuzzy logic model performs group evaluations, unlike current assessments, which are carried out independently one by one. Generating all the evaluations at the same time allows a graph with the global behaviour pattern to be generated, which serves the specialist in decision making to improve tasks so that the risk for the majority of the workers is minimised.

To achieve these results, we developed a decision support system that incorporates 54 membership equations for operations involving fuzzy sets. This system is important for evaluating how anthropometry and biomechanics affect ergonomic assessments and to what extent. The behavioural pattern of the group of 123 evaluations changes as risk value is added. For example, in Test 1, a low-risk task was analysed, so a biomechanical risk pattern inherent only to the worker’s anthropometry was observed. In Test 2, a medium-risk task was analysed; in this case, the pattern of evaluations changed, and behaviour more affected by anthropometric and biomechanical characteristics was seen, although the trend was not yet very clear. Finally, in Test 3, the influence of anthropometry and biomechanics was clearly observed in the pattern of risk assessments, which followed the same shape as the anthropometric set.

While the research objectives were achieved, the system requires improvement to enhance the accuracy of the evaluation. Currently, the DSS lacks some necessary information, so future efforts are suggested to refine the system and extend it applicability to other body parts. Artificial intelligence can be integrated initially as training software, followed by its implementation as an evaluation system.

This model enhances the current theoretical framework by managing an infinite number of combinations without requiring the development of fuzzy rules, which can become numerous when combining various task elements. It incorporates the necessary components to compete effectively with risk assessments that analyse the same factors. This system is more accurate because it directly measures and utilises the worker’s biomechanical and anthropometric values. It improves precision and offers a risk measurement system useful for users who may not be very familiar with such calculations.

Finally, by utilising the fuzzy model, we can identify at least three types of suggestions for the improvement process and polices:

• Improving work tasks enables the establishment of minimum, average, and maximum parameters within which these tasks can be performed without risking musculoskeletal disorders.
• Taking anthropometric and biomechanic risks into account allows for the redesign of work areas based on the characteristics of the users.
• From a social responsibility standpoint, understanding body mass index (BMI) can help generate internal policies that promote healthy eating among employees.

5. Conclusions

In conclusion, the fuzzy model developed for ergonomic assessments is a valuable tool for industries requiring user-friendly and accessible solutions. It was created in Excel, as this software is commonly available in most companies, in contrast to other scientific programs like Wolfram Mathematica or MATLAB, which would incur additional licensing costs for users. This tool facilitates simultaneous risk assessments by simply entering the anthropometric data of the workers involved and information about the work methods. The result is a tailored ergonomic risk assessment for each worker, based on their individual biomechanics and anthropometry, making it more accurate than other assessments that rely on generic characteristics.